Answer:
[tex]\displaystyle \lim_{x \to \infty} \frac{\sqrt{x} + x^2}{5x - x^2} = -1[/tex]
General Formulas and Concepts:
Calculus
Limits
Step-by-step explanation:
We are given the following limit:
[tex]\displaystyle \lim_{x \to \infty} \frac{\sqrt{x} + x^2}{5x - x^2}[/tex]
We can use the Coefficient Power Method to solve this. Since both the numerator and the denominator have the same power, we simply divide the coefficients to get our answer:
[tex]\displaystyle \lim_{x \to \infty} \frac{\sqrt{x} + x^2}{5x - x^2} = \frac{1}{-1}[/tex]
Simplifying it, we have:
[tex]\displaystyle \lim_{x \to \infty} \frac{\sqrt{x} + x^2}{5x - x^2} = -1[/tex]
And we arrive at our answer.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
